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Conjecture- unproven statement that is
based on observations.
 Inductive reasoning- looking for patterns
and making conjectures is part of this
process
 Counterexample- example shows a
conjecture is false.

Point- no dimensions.
 Line- extends in one dimension.
 Plane- extends in two directions.
 Collinear points- points that lie on the
same line.
 Coplanar points- points that lie on the
same plane.







Acute angles- less than 90 degrees
Right angles- equal to 90 degrees
Obtuse angles- more than 90 degrees
Straight angles- equal to 180 degrees
Complementary angles- sum of measures is
90 degrees.
Supplementary angles- sum of measures is
180 degrees.

Distance Formula-
› AB=Square root of(x-x1)²+(y2-y1)²

Pythagorean Theorem-
a²+b²=c²
Parallel lines-coplanar and do not intersect.
 Transversal- a line that intersects two or more
coplanar lines at different points.
 Corresponding angles- if they occupy
corresponding positions.
 Alternate exterior angles- if they lie outside the two
lines on opposite sides of the transversal.
 Alternate interior angles- if they lie between the
two lines on opposite sides of the transversal.
 Consecutive interior angles- if they lie between the
two lines on the same side of the transversal.


Theorem 3.1
› If two lines intersect to form a linear pair of
congruent angles, then the lines are
perpendicular.

Theorem 3.2
› If two sides of two adjacent acute angles are
perpendicular, then the angles are
complementary.

Theorem 3.3
› If two lines are perpendicular, then they intersect
to form four right angles.



Theorem 3.4- Alternate Interior Angles
› If two parallel lines are cut by a transversal, then
the pairs of alternate interior angles are
congruent.
Theorem 3.5- Consecutive Interior Angles
› If two parallel lines are cut by a transversal, then
the pairs of consecutive interior angles are
supplementary.
Theorem 3.6- Alternate Exterior Angles
› If two parallel lines are cut by a transversal, then
the pairs of alternate exterior angles are
congruent.
Vertex- each of the three points joining
the sides of a triangle.
 Adjacent sides- two sides sharing a
common vertex.
 Hypotenuse- side opposite of the right
angle.
 Congruent- correspondence between
their angles and sides.


Names of Triangles
› Equilateral
› Isosceles
› Scalene

Classification by angles
› Acute
› Equiangular
› Right
› Obtuse

Reflexive Property
› Every triangle is congruent to itself.

Symmetric Property
› If triangle ABC is congruent to triangle DEF, the
triangle DEF is congruent to triangle ABC.

Transitive Property
› If triangle ABC is congruent to triangle DEF and
triangle DEF is congruent to triangle JKL, then
triangle ABC is congruent to triangle JKL.

Side- Side-Side

Side-Angle-Side

Angle-Side-Angle

Angle-Angle-Side

Convex- if no line that contains a side of the
polygon contains a point in the interior of the
polygon.
Concave- a polygon that is not convex.
 Diagonal- a segment that joins two

nonconsecutive vertices.

Theorem 6.6
› If both pairs of opposite sides of a quadrilateral
are congruent, then the quadrilateral is a
parallelogram.

Theorem 6.7
› If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.

Theorem 6.8
› If an angle of a quadrilateral is supplementary
to both of its consecutive angles, then the
quadrilateral is a parallelogram.
Preimage- original figure.
 Image- new figure
 Transformation- operation that moves
the preimage to the image.
 Translation- a transformation that maps
every two points.


Theorem 7.2 Rotation Theorem
› A rotation is an isometry.

Theorem 7.3
› If lines k and m intersect at point P, then a
reflection in k followed by a reflection in m is
a rotation about point P.
Proportion- an equation that equates two ratios.
 Geometric mean- two positive numbers a and

b is the positive number x such that a/x=x/b.

Similar polygons- when there is a
correspondence between two polygons such that
their corresponding angles are congruent and the
lengths of corresponding sides are proportional.

Side-Side-Side
› If the lengths of the corresponding sides of
two triangles are proportional, then the
triangles are similar.

Side-Angle-Side
› If an angle of one triangle is congruent to an
angle of a second triangle and the lengths
of the sides including these angles are
proportional, then the triangles are similar.
Special right triangles- have measures of
45-45-90 or 30-60-90.
 Sin, cosine, tangent- three basic
trigonometric ratios.
 Trigonometric ratio- ratio of the lengths
of two sides of a right triangle.


Theorem 9.8 45-45-90 Triangle
› In a 45-45-90 triangle, the hypotenuse is
square root of 2 times as long as each leg.

Theorem 9.9 30-60-90 Triangle
› In a 30-60-90 triangle, the hypotenuse is
twice as long as the shorter leg, and the
longer leg is square root of 3 times as long as
the shorter leg.
Diameter- distance across the circle.
 Radius- distance from center to point on
the circle.
 Chord- segment whose endpoints are
points on the circle.
 Secant- a line that intersects a circle in
two points.
 Tangent- a line in the plane of a circle
that intersects the circle in exactly one
point.

Minor arc- part of a circle that measures
less than 180 degrees.
 Major arc- part of a circle that measures
between 180 degrees and 360 degrees.
 Semicircle- if the endpoints of an arc are
the endpoints of diameter, then it is a
semicircle.


Theorem 10.1
› If a line is tangent to a circle, then it is
perpendicular to the radius drawn to the
point of tangency.

Theorem 10.2
› In a plane, if a line is perpendicular to a
radius if a circle at its endpoint on the circle,
then the line is tangent to the circle.
Circumference- is the distance around
the circle.
 Arc length- portion of the circumference
of a circle.
 Semicircle- one half of the
circumference.
 To find the sum of the measures of
interior angles of a polygon
› 180 multiplied by the number of sides.

Given that the radius of the circle is 5 cm, calculate the area
of the shaded sector. (Take π = 3.142).
Area of Sector=
=13.09cm²

Finding Arc Length
Or you can use
this step:

Theorem 11.4 – Area of Regular Polygons
› The area of a regular n-gon with side length s
is half the product of the apothem a and the
perimeter P, so A=(1/2)aP or A=(1/2)aXns.

Theorem 11.8
› The ratio of the area A of a sector of a circle
to the area of the circle is equal to the ratio
of the measure of the intercepted arc to 360
degrees.
Faces- a solid that is bounded by
polygons.
 Edge- line segment formed by the
intersection of two faces.
 Vertex- point where three or more edges
meet.
